SlaKoNet-VQD: A universal Slater-Koster tight-binding Hamiltonian for variational quantum band-structure calculations on near-term hardware

Abstract

Variational quantum algorithms such as VQE and VQD are promising for near-term electronic structure calculations, but for periodic solids their reach is limited by the cost of building a faithful second-quantized Hamiltonian, typically via DFT plus Wannierization or hand-fit tight-binding parameters. SlaKoNet addresses this by combining deep learning with the Slater-Koster tight-binding formalism to fit hopping and overlap parameters across 65 elements, enabling deterministic Hamiltonian construction for any crystal built from these elements. Here we couple a SlaKoNet model trained on JARVIS-TBmBJ with a Qiskit-based VQD algorithm, replacing costly Hamiltonian construction with a universal neural Hamiltonian generator. The resulting SlaKoNet-VQD workflow is structure-agnostic, differentiable, and suited to high-throughput bandstructure screening. We benchmark on silicon, recovering the full eight-band structure along the standard k-path with mean absolute deviation of 1.78 meV from exact diagonalization on a 3-qubit simulator, and extend to five conventional superconductors (Al, Ta, Nb, V, ZrN) with similar accuracy. We demonstrate execution on IBM Quantum hardware for a k-point ground-state calculation on aluminum (MAE ~0.37 eV). We further promote the Hamiltonian to a correlated Hubbard model solved via dynamical mean-field theory, recovering weakening correlations across group-5 metals and strong quasiparticle renormalization in La2CuO4, identifying the impurity problem as a natural quantum solver target. This pipeline enables high-throughput VQA benchmarking across the periodic table and gradient-based ansatz-Hamiltonian co-optimization for materials discovery. Web app: https://atomgpt.org/quantum.